A sequence of random variables {Xi} such that the expected value of the (n + 1)th random variable, once the first n outcomes are known, is just the current value Xn. The simple random walk, which moves left or right one step with probability 0.5, is an example of a martingale.
The sequence of random variables X1, X2,…(with finite expected values) is a martingale if the conditional expected value of Xn+1, given the values of X1, X2,…, Xn, is given by
An example is provided by letting Xn be the amount of a gambler's winnings after the nth of a sequence of fair games.
A stochastic process in which the expectation of the future value of a variable, conditional on currently available information, including the current value, is equal to the current value of the variable.
- ambient computing
- ambient light
- ambient pressure
- ambient temperature
- ambiguity
- ambiguity rule
- ambiguous case
- ambiguous grammar
- ambiguous middle, fallacy of
- ambipolar diffusion
- ambisonics
- ambitus
- ambivalence
- ambo-
- Ambrose, St (340–97)
- Ambrose, St (c.339–97)
- ambulacral
- ambulacral groove
- ambulacrum
- Ambulocetus natans
- AM Canum Venaticorum star
- AM detector
- ameloblast
- Amenhotep
- amenity